Both men have been arrested by Israeli security forces before, according to an ISA news release. Kawasmeh served a 10-month prison sentence.

"In his most recent investigation, in 2010, (Kawasmeh) admitted to having been recruited to the Hamas military wing in the Hebron area in 2009," ISA said. Abu-Isa was detained several times between 2005 and 2007.

House to house search for missing teens

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Israeli PM says Hamas abducted 3 teens

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Photo of three missing Israeli settlers the IDF says were kidnapped in the West Bank. Gilad Shaer, Naftali Frenkel and Eyal Yifrach.

Lt. Col. Peter Lerner of the Israel Defense Forces said Thursday that both men have "a history of terrorist activity" and both were "suspects immediately after the kidnapping."

The three teenagers, Gilad Shaar and Naftali Frenkel, both 16, and Eyal Yifrach, 19, were last seen around Gush Etzion, on the Israeli side of the West Bank barrier late on June 12 or early on June 13, according to the IDF.

After the release of the suspects' identities, Prime Minister Benjamin Netanyahu responded with a comment directed at Palestinian Authority President Mahmoud Abbas.

"I now expect President Abbas ... to break his pact with the Hamas terrorist organization that kidnaps children and calls for the destruction of Israel."

Previously Abbas had condemned the kidnappings and called on all sides to refrain from violence, according to an Israeli newspaper report earlier this month.

Netanyahu blamed Hamas for the kidnappings almost immediately. A Hamas spokesman said in the days after the abductions that Netanyahu's comments attributing blame were "stupid and baseless."

Israeli security forces have conducted an extensive search for the teens. Within days after the teens' disappearance, Israeli soldiers had detained more than 150 Palestinian suspects. The military said Hamas leaders and operatives were among the suspects.

As the search for the two suspects continues, the IDF and ISA said Thursday several other suspects are also being questioned "for their personal involvement of the attack."